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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 458640o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 458640.o1 | 458640o1 | \([0, 0, 0, -475960863, 3996913155662]\) | \(-11083722100790228176/582924346875\) | \(-627139287892079071200000\) | \([]\) | \(99993600\) | \(3.6346\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 458640o1 has rank \(1\).
Complex multiplication
The elliptic curves in class 458640o do not have complex multiplication.Modular form 458640.2.a.o
sage: E.q_eigenform(10)